Geometry Flashcards
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Geometry Flashcards

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Questions and Answers

What geometric term is modeled by a tight rope?

  • Segment
  • Plane
  • Line (correct)
  • Point
  • What geometric term is modeled by a floor?

  • Line
  • Point
  • Segment
  • Plane (correct)
  • What geometric term is modeled by a button?

  • Point (correct)
  • Plane
  • Segment
  • Line
  • What is the definition of a segment?

    <p>A defined term</p> Signup and view all the answers

    What is a point in geometry?

    <p>An undefined term in geometry, it names a location and has no size.</p> Signup and view all the answers

    What is the definition of a line?

    <p>An undefined term in geometry, it is a straight path that has no thickness and extends forever.</p> Signup and view all the answers

    What is a plane in geometry?

    <p>An undefined term in geometry that is a flat surface that has no thickness and extends forever.</p> Signup and view all the answers

    What is a line segment?

    <p>A part of a line consisting of two endpoints and all the space between them.</p> Signup and view all the answers

    What is an endpoint?

    <p>A point at an end of a segment or the starting point of a ray.</p> Signup and view all the answers

    What is a ray?

    <p>A part of a line that starts at an endpoint and extends forever in one direction.</p> Signup and view all the answers

    What does coplanar mean?

    <p>Points that lie in the same plane.</p> Signup and view all the answers

    What does parallel mean in geometry?

    <p>Lines or planes that do not intersect.</p> Signup and view all the answers

    What does collinear refer to?

    <p>Points that lie on the same line.</p> Signup and view all the answers

    What is a postulate?

    <p>A statement that is accepted as true without proof.</p> Signup and view all the answers

    What is a midpoint?

    <p>The point that divides a segment into two congruent segments.</p> Signup and view all the answers

    What is a segment bisector?

    <p>A line, ray, or segment that divides a segment into two congruent segments.</p> Signup and view all the answers

    What is an angle?

    <p>A figure formed by two rays with a common endpoint.</p> Signup and view all the answers

    What is a vertex in geometry?

    <p>The common endpoint of the sides of an angle.</p> Signup and view all the answers

    What is a side in relation to angles?

    <p>One of the two rays that form an angle.</p> Signup and view all the answers

    What unit is used to measure angles?

    <p>Degrees</p> Signup and view all the answers

    What is an angle bisector?

    <p>A ray, line, or segment that divides an angle into two congruent angles.</p> Signup and view all the answers

    What does transformation mean in geometry?

    <p>A change in the position, size, or shape of a figure.</p> Signup and view all the answers

    What is a preimage?

    <p>The original figure in a transformation.</p> Signup and view all the answers

    What is an image in geometry?

    <p>A shape that results from the transformation of a preimage.</p> Signup and view all the answers

    What is a rigid motion?

    <p>A transformation of the plane or space, which preserves distance and angles.</p> Signup and view all the answers

    What is a conjecture?

    <p>A statement that is believed to be true.</p> Signup and view all the answers

    What is inductive reasoning?

    <p>A process of reasoning that a rule or statement is true because specific cases are true.</p> Signup and view all the answers

    What is deductive reasoning?

    <p>A process of reasoning using logic to draw conclusions.</p> Signup and view all the answers

    What is a theorem?

    <p>A statement that has been proven.</p> Signup and view all the answers

    What is a counterexample?

    <p>An example that proves that a conjecture or statement is false.</p> Signup and view all the answers

    What is a conditional statement?

    <p>A statement that can be written in the 'if p, then q' form, where p is the hypothesis and q is the conclusion.</p> Signup and view all the answers

    What is a linear pair?

    <p>A pair of adjacent angles whose noncommon sides are opposite rays.</p> Signup and view all the answers

    What is a converse statement?

    <p>A statement formed by exchanging the hypothesis and the conclusion of a conditional statement.</p> Signup and view all the answers

    What is an inverse statement?

    <p>A statement formed by negating the hypothesis and conclusion of a conditional statement.</p> Signup and view all the answers

    What is a biconditional statement?

    <p>A statement that can be written in the form, 'p if and only if q.'</p> Signup and view all the answers

    What is the reflexive property?

    <p>a=a</p> Signup and view all the answers

    What is the symmetric property?

    <p>if a=b, then b=a</p> Signup and view all the answers

    What is the transitive property?

    <p>If a=b and b=c, then a=c</p> Signup and view all the answers

    What is the substitution property?

    <p>If a=b, then b can take the place of a in any expression.</p> Signup and view all the answers

    What is the addition property?

    <p>If a=b, then a+c=b+c</p> Signup and view all the answers

    What is the subtraction property?

    <p>If a=b, then a-c=b-c</p> Signup and view all the answers

    What is the multiplication property?

    <p>If a=b, then ac=bc</p> Signup and view all the answers

    What is the division property?

    <p>If a=b and c≠0, then a/c=b/c</p> Signup and view all the answers

    Study Notes

    Basic Geometry Terms

    • Point: An undefined term representing a specific location with no dimensions.
    • Line: An undefined term defined as a straight path without thickness, extending indefinitely.
    • Plane: An undefined term defined as a flat surface with no thickness, extending infinitely in all directions.

    Defined Geometry Terms

    • Segment: A part of a line with two endpoints and all the points in between.
    • Line Segment: Specifically defined as a segment limited by two endpoints.
    • Ray: A part of a line that starts at a designated endpoint and continues indefinitely in one direction.
    • Endpoint: The terminal point of a line segment or the start of a ray.
    • Coplanar: Term used to describe points that lie within the same geometric plane.
    • Collinear: Refers to points that all lie on the same straight line.

    Angles and Their Properties

    • Angle: Formed by two rays sharing a common endpoint called the vertex.
    • Vertex: The shared endpoint of the rays forming an angle.
    • Sides: The rays that combine to form an angle.
    • Degrees: The unit of measurement used to quantify angles.
    • Angle Bisector: A ray or line that divides an angle into two equal angles.

    Postulates and Theorems

    • Postulate: A foundational statement accepted as true without proof.
    • Theorem: A statement proven based on previously established axioms and postulates.
    • Conjecture: A statement believed to be true based on evidence or reasoning.
    • Counterexample: An example used to demonstrate that a conjecture is false.

    Reasoning Methods

    • Inductive Reasoning: Involves drawing general conclusions based on specific cases.
    • Deductive Reasoning: Logical reasoning from general premises to reach a specific conclusion.

    Relationships Between Angles

    • Linear Pair: Two adjacent angles whose noncommon sides form opposite rays.
    • Converse: A statement created by swapping the hypothesis and conclusion of a conditional.
    • Inverse: A statement generated by negating both the hypothesis and conclusion of a conditional statement.
    • Biconditional Statement: A statement that is true in both directions, represented as "p if and only if q."

    Geometry Transformations

    • Transformation: Changes the position, size, or shape of a figure.
    • Preimage: The original figure before transformation.
    • Image: The resultant figure after transformation.
    • Rigid Motion: A transformation maintaining distances and angles.

    Measurement and Properties

    • Midpoint: The point that equally divides a segment into two congruent parts.
    • Segment Bisector: A line, ray, or segment that intersects another segment at its midpoint.
    • Distance Formula: A method for calculating the distance between two points in a coordinate plane.
    • Midpoint Formula: A calculation to find the midpoint between two points in a coordinate plane.

    Algebraic Properties

    • Reflexive Property: States that any quantity is equal to itself (a = a).
    • Symmetric Property: If one quantity equals another, then the second equals the first (if a = b, then b = a).
    • Transitive Property: If one quantity equals a second and that second equals a third, the first equals the third (if a = b and b = c, then a = c).
    • Substitution Property: If two quantities are equal, one can be substituted for the other in any expression.
    • Addition Property: If two quantities are equal, adding the same value to both preserves equality (if a = b, then a + c = b + c).
    • Subtraction Property: If two quantities are equal, subtracting the same value from both maintains the equality (if a = b, then a - c = b - c).
    • Multiplication Property: If two quantities are equal, multiplying both by the same number keeps them equal (if a = b, then ac = bc).
    • Division Property: If two quantities are equal, dividing both by the same non-zero value keeps the equality (if a = b and c ≠ 0, then a/c = b/c).

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    Test your knowledge of fundamental geometric terms with these flashcards. Each card presents a word and its corresponding definition, helping you to memorize important concepts in geometry. Whether you're a student preparing for exams or just brushing up on your skills, these flashcards are a great tool.

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